LMFDB - Embedded newform 896.2.u.c.337.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [896,2,Mod(113,896)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(896, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([0, 1, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("896.113");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 896 = 2^{7} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	896.u (of order $8$, degree $4$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$7.15459602111$
Analytic rank:	$0$
Dimension:	$52$
Relative dimension:	$13$ over $\Q(\zeta_{8})$
Twist minimal:	no (minimal twist has level 224)
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			337.7
Character	$\chi$	$=$	896.337
Dual form			896.2.u.c.561.7

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.301186 + 0.124755i) q^{3} +(-0.107860 - 0.260396i) q^{5} +(-0.707107 + 0.707107i) q^{7} +(-2.04617 - 2.04617i) q^{9} +O(q^{10})$	\(q+(0.301186 + 0.124755i) q^{3} +(-0.107860 - 0.260396i) q^{5} +(-0.707107 + 0.707107i) q^{7} +(-2.04617 - 2.04617i) q^{9} +(-3.69299 + 1.52969i) q^{11} +(1.11577 - 2.69371i) q^{13} -0.0918835i q^{15} +2.71818i q^{17} +(2.79192 - 6.74030i) q^{19} +(-0.301186 + 0.124755i) q^{21} +(-4.62688 - 4.62688i) q^{23} +(3.47936 - 3.47936i) q^{25} +(-0.735272 - 1.77510i) q^{27} +(-7.01178 - 2.90438i) q^{29} -8.98987 q^{31} -1.30311 q^{33} +(0.260396 + 0.107860i) q^{35} +(-0.290547 - 0.701441i) q^{37} +(0.672109 - 0.672109i) q^{39} +(8.31028 + 8.31028i) q^{41} +(4.89311 - 2.02679i) q^{43} +(-0.312116 + 0.753514i) q^{45} +3.02069i q^{47} -1.00000i q^{49} +(-0.339107 + 0.818676i) q^{51} +(2.02051 - 0.836925i) q^{53} +(0.796649 + 0.796649i) q^{55} +(1.68177 - 1.68177i) q^{57} +(-3.56490 - 8.60644i) q^{59} +(-8.50594 - 3.52327i) q^{61} +2.89372 q^{63} -0.821779 q^{65} +(-0.268430 - 0.111187i) q^{67} +(-0.816323 - 1.97078i) q^{69} +(-0.708001 + 0.708001i) q^{71} +(-7.22072 - 7.22072i) q^{73} +(1.48200 - 0.613865i) q^{75} +(1.52969 - 3.69299i) q^{77} +11.6234i q^{79} +8.05481i q^{81} +(3.02245 - 7.29684i) q^{83} +(0.707802 - 0.293181i) q^{85} +(-1.74951 - 1.74951i) q^{87} +(-2.37079 + 2.37079i) q^{89} +(1.11577 + 2.69371i) q^{91} +(-2.70762 - 1.12153i) q^{93} -2.05628 q^{95} -8.85759 q^{97} +(10.6865 + 4.42649i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 52 q+O(q^{10}) $ 52 * q	$ 52 q + 20 q^{23} + 24 q^{27} - 48 q^{33} + 24 q^{39} + 44 q^{43} + 40 q^{45} - 16 q^{51} - 36 q^{53} - 32 q^{55} - 32 q^{61} - 68 q^{63} + 80 q^{65} - 28 q^{67} - 32 q^{69} - 32 q^{75} - 12 q^{77} + 64 q^{85} + 56 q^{87} + 64 q^{95} - 72 q^{97} + 64 q^{99}+O(q^{100}) $ 52 * q + 20 * q^23 + 24 * q^27 - 48 * q^33 + 24 * q^39 + 44 * q^43 + 40 * q^45 - 16 * q^51 - 36 * q^53 - 32 * q^55 - 32 * q^61 - 68 * q^63 + 80 * q^65 - 28 * q^67 - 32 * q^69 - 32 * q^75 - 12 * q^77 + 64 * q^85 + 56 * q^87 + 64 * q^95 - 72 * q^97 + 64 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/896\mathbb{Z}\right)^\times$.

$n$	$127$	$129$	$645$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{8}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	0.301186	+	0.124755i	0.173890	+	0.0720274i	0.467930	−	0.883766i	$-0.345000\pi$
$3$	0.301186	+	0.124755i	0.173890	+	0.0720274i	−0.294040	+	0.955793i	$0.595000\pi$
$4$		0			0
$5$	−0.107860	−	0.260396i	−0.0482363	−	0.116453i	0.897925	−	0.440149i	$-0.145074\pi$
$5$	−0.107860	−	0.260396i	−0.0482363	−	0.116453i	−0.946161	+	0.323696i	$0.895074\pi$
$6$		0			0
$7$	−0.707107	+	0.707107i	−0.267261	+	0.267261i
$7$	−0.707107	+	0.707107i	−0.267261	+	0.267261i
$8$		0			0
$9$	−2.04617	−	2.04617i	−0.682057	−	0.682057i
$10$		0			0
$11$	−3.69299	+	1.52969i	−1.11348	+	0.461218i	−0.862135	−	0.506679i	$-0.830873\pi$
$11$	−3.69299	+	1.52969i	−1.11348	+	0.461218i	−0.251345	+	0.967898i	$0.580873\pi$
$12$		0			0
$13$	1.11577	−	2.69371i	0.309460	−	0.747102i	−0.690263	−	0.723559i	$-0.742505\pi$
$13$	1.11577	−	2.69371i	0.309460	−	0.747102i	0.999723	−	0.0235435i	$-0.00749482\pi$
$14$		0			0
$15$		−	0.0918835i		−	0.0237242i
$16$		0			0
$17$			2.71818i			0.659255i	0.944111	+	0.329627i	$0.106923\pi$
$17$			2.71818i			0.659255i	−0.944111	+	0.329627i	$0.893077\pi$
$18$		0			0
$19$	2.79192	−	6.74030i	0.640511	−	1.54633i	−0.185480	−	0.982648i	$-0.559384\pi$
$19$	2.79192	−	6.74030i	0.640511	−	1.54633i	0.825991	−	0.563683i	$-0.190616\pi$
$20$		0			0
$21$	−0.301186	+	0.124755i	−0.0657241	+	0.0272238i
$22$		0			0
$23$	−4.62688	−	4.62688i	−0.964772	−	0.964772i	0.0346283	−	0.999400i	$-0.488975\pi$
$23$	−4.62688	−	4.62688i	−0.964772	−	0.964772i	−0.999400	+	0.0346283i	$0.988975\pi$
$24$		0			0
$25$	3.47936	−	3.47936i	0.695872	−	0.695872i
$26$		0			0
$27$	−0.735272	−	1.77510i	−0.141503	−	0.341619i
$28$		0			0
$29$	−7.01178	−	2.90438i	−1.30206	−	0.539329i	−0.379499	−	0.925192i	$-0.623904\pi$
$29$	−7.01178	−	2.90438i	−1.30206	−	0.539329i	−0.922556	+	0.385863i	$0.873904\pi$
$30$		0			0
$31$	−8.98987			−1.61463			−0.807314	−	0.590122i	$-0.799080\pi$
$31$	−8.98987			−1.61463			−0.807314	+	0.590122i	$0.799080\pi$
$32$		0			0
$33$	−1.30311			−0.226843
$34$		0			0
$35$	0.260396	+	0.107860i	0.0440149	+	0.0182316i
$36$		0			0
$37$	−0.290547	−	0.701441i	−0.0477656	−	0.115316i	0.898196	−	0.439596i	$-0.144878\pi$
$37$	−0.290547	−	0.701441i	−0.0477656	−	0.115316i	−0.945961	+	0.324279i	$0.894878\pi$
$38$		0			0
$39$	0.672109	−	0.672109i	0.107624	−	0.107624i
$40$		0			0
$41$	8.31028	+	8.31028i	1.29785	+	1.29785i	0.929812	+	0.368036i	$0.119970\pi$
$41$	8.31028	+	8.31028i	1.29785	+	1.29785i	0.368036	+	0.929812i	$0.380030\pi$
$42$		0			0
$43$	4.89311	−	2.02679i	0.746193	−	0.309083i	0.0230057	−	0.999735i	$-0.492676\pi$
$43$	4.89311	−	2.02679i	0.746193	−	0.309083i	0.723187	+	0.690652i	$0.242676\pi$
$44$		0			0
$45$	−0.312116	+	0.753514i	−0.0465275	+	0.112327i
$46$		0			0
$47$			3.02069i			0.440612i	0.975431	+	0.220306i	$0.0707057\pi$
$47$			3.02069i			0.440612i	−0.975431	+	0.220306i	$0.929294\pi$
$48$		0			0
$49$		−	1.00000i		−	0.142857i
$50$		0			0
$51$	−0.339107	+	0.818676i	−0.0474844	+	0.114638i
$52$		0			0
$53$	2.02051	−	0.836925i	0.277539	−	0.114960i	−0.239572	−	0.970878i	$-0.577007\pi$
$53$	2.02051	−	0.836925i	0.277539	−	0.114960i	0.517111	+	0.855918i	$0.327007\pi$
$54$		0			0
$55$	0.796649	+	0.796649i	0.107420	+	0.107420i
$56$		0			0
$57$	1.68177	−	1.68177i	0.222756	−	0.222756i
$58$		0			0
$59$	−3.56490	−	8.60644i	−0.464111	−	1.12046i	−0.966694	−	0.255934i	$-0.917617\pi$
$59$	−3.56490	−	8.60644i	−0.464111	−	1.12046i	0.502583	−	0.864529i	$-0.332383\pi$
$60$		0			0
$61$	−8.50594	−	3.52327i	−1.08907	−	0.451109i	−0.235390	−	0.971901i	$-0.575637\pi$
$61$	−8.50594	−	3.52327i	−1.08907	−	0.451109i	−0.853684	+	0.520792i	$0.825637\pi$
$62$		0			0
$63$	2.89372			0.364575
$64$		0			0
$65$	−0.821779			−0.101929
$66$		0			0
$67$	−0.268430	−	0.111187i	−0.0327939	−	0.0135837i	0.366226	−	0.930526i	$-0.380650\pi$
$67$	−0.268430	−	0.111187i	−0.0327939	−	0.0135837i	−0.399020	+	0.916942i	$0.630650\pi$
$68$		0			0
$69$	−0.816323	−	1.97078i	−0.0982737	−	0.237254i
$70$		0			0
$71$	−0.708001	+	0.708001i	−0.0840243	+	0.0840243i	−0.747870	−	0.663845i	$-0.768923\pi$
$71$	−0.708001	+	0.708001i	−0.0840243	+	0.0840243i	0.663845	+	0.747870i	$0.268923\pi$
$72$		0			0
$73$	−7.22072	−	7.22072i	−0.845122	−	0.845122i	0.144398	−	0.989520i	$-0.453875\pi$
$73$	−7.22072	−	7.22072i	−0.845122	−	0.845122i	−0.989520	+	0.144398i	$0.953875\pi$
$74$		0			0
$75$	1.48200	−	0.613865i	0.171127	−	0.0708830i
$76$		0			0
$77$	1.52969	−	3.69299i	0.174324	−	0.420856i
$78$		0			0
$79$			11.6234i			1.30774i	0.756607	+	0.653870i	$0.226855\pi$
$79$			11.6234i			1.30774i	−0.756607	+	0.653870i	$0.773145\pi$
$80$		0			0
$81$			8.05481i			0.894978i
$82$		0			0
$83$	3.02245	−	7.29684i	0.331757	−	0.800932i	−0.666696	−	0.745330i	$-0.732292\pi$
$83$	3.02245	−	7.29684i	0.331757	−	0.800932i	0.998453	−	0.0556024i	$-0.0177079\pi$
$84$		0			0
$85$	0.707802	−	0.293181i	0.0767719	−	0.0318000i
$86$		0			0
$87$	−1.74951	−	1.74951i	−0.187567	−	0.187567i
$88$		0			0
$89$	−2.37079	+	2.37079i	−0.251303	+	0.251303i	−0.821505	−	0.570202i	$-0.806865\pi$
$89$	−2.37079	+	2.37079i	−0.251303	+	0.251303i	0.570202	+	0.821505i	$0.306865\pi$
$90$		0			0
$91$	1.11577	+	2.69371i	0.116965	+	0.282378i
$92$		0			0
$93$	−2.70762	−	1.12153i	−0.280767	−	0.116297i
$94$		0			0
$95$	−2.05628			−0.210970
$96$		0			0
$97$	−8.85759			−0.899352			−0.449676	−	0.893192i	$-0.648461\pi$
$97$	−8.85759			−0.899352			−0.449676	+	0.893192i	$0.648461\pi$
$98$		0			0
$99$	10.6865	+	4.42649i	1.07403	+	0.444879i
$100$		0			0
$101$	−0.685667	−	1.65535i	−0.0682264	−	0.164713i	0.886088	−	0.463517i	$-0.153413\pi$
$101$	−0.685667	−	1.65535i	−0.0682264	−	0.164713i	−0.954315	+	0.298803i	$0.903413\pi$
$102$		0			0
$103$	0.223645	−	0.223645i	0.0220364	−	0.0220364i	−0.696003	−	0.718039i	$-0.745040\pi$
$103$	0.223645	−	0.223645i	0.0220364	−	0.0220364i	0.718039	+	0.696003i	$0.245040\pi$
$104$		0			0
$105$	0.0649715	+	0.0649715i	0.00634057	+	0.00634057i
$106$		0			0
$107$	3.99560	−	1.65503i	0.386269	−	0.159998i	−0.181094	−	0.983466i	$-0.557964\pi$
$107$	3.99560	−	1.65503i	0.386269	−	0.159998i	0.567363	+	0.823468i	$0.307964\pi$
$108$		0			0
$109$	4.95301	−	11.9576i	0.474412	−	1.14533i	−0.487781	−	0.872966i	$-0.662194\pi$
$109$	4.95301	−	11.9576i	0.474412	−	1.14533i	0.962194	−	0.272366i	$-0.0878063\pi$
$110$		0			0
$111$		−	0.247511i		−	0.0234927i
$112$		0			0
$113$			5.75451i			0.541339i	0.962672	+	0.270669i	$0.0872450\pi$
$113$			5.75451i			0.541339i	−0.962672	+	0.270669i	$0.912755\pi$
$114$		0			0
$115$	−0.705768	+	1.70388i	−0.0658132	+	0.158887i
$116$		0			0
$117$	−7.79487	+	3.22874i	−0.720636	+	0.298497i
$118$		0			0
$119$	−1.92204	−	1.92204i	−0.176193	−	0.176193i
$120$		0			0
$121$	3.52008	−	3.52008i	0.320007	−	0.320007i
$122$		0			0
$123$	1.46619	+	3.53969i	0.132202	+	0.319163i
$124$		0			0
$125$	−2.58327	−	1.07003i	−0.231055	−	0.0957061i
$126$		0			0
$127$	8.48085			0.752553			0.376277	−	0.926507i	$-0.377204\pi$
$127$	8.48085			0.752553			0.376277	+	0.926507i	$0.377204\pi$
$128$		0			0
$129$	1.72659			0.152018
$130$		0			0
$131$	18.1306	+	7.50993i	1.58408	+	0.656146i	0.989053	−	0.147563i	$-0.0471428\pi$
$131$	18.1306	+	7.50993i	1.58408	+	0.656146i	0.595023	+	0.803708i	$0.297143\pi$
$132$		0			0
$133$	2.79192	+	6.74030i	0.242091	+	0.584458i
$134$		0			0
$135$	−0.382924	+	0.382924i	−0.0329568	+	0.0329568i
$136$		0			0
$137$	10.2482	+	10.2482i	0.875560	+	0.875560i	0.993071	−	0.117512i	$-0.0374918\pi$
$137$	10.2482	+	10.2482i	0.875560	+	0.875560i	−0.117512	+	0.993071i	$0.537492\pi$
$138$		0			0
$139$	−12.8093	+	5.30580i	−1.08647	+	0.450032i	−0.852776	−	0.522277i	$-0.825083\pi$
$139$	−12.8093	+	5.30580i	−1.08647	+	0.450032i	−0.233698	+	0.972309i	$0.575083\pi$
$140$		0			0
$141$	−0.376846	+	0.909787i	−0.0317362	+	0.0766179i
$142$		0			0
$143$			11.6547i			0.974611i
$144$		0			0
$145$			2.13910i			0.177643i
$146$		0			0
$147$	0.124755	−	0.301186i	0.0102896	−	0.0248414i
$148$		0			0
$149$	2.47617	−	1.02567i	0.202856	−	0.0840258i	−0.278942	−	0.960308i	$-0.589984\pi$
$149$	2.47617	−	1.02567i	0.202856	−	0.0840258i	0.481798	+	0.876282i	$0.339984\pi$
$150$		0			0
$151$	1.03771	+	1.03771i	0.0844477	+	0.0844477i	0.748069	−	0.663621i	$-0.230981\pi$
$151$	1.03771	+	1.03771i	0.0844477	+	0.0844477i	−0.663621	+	0.748069i	$0.730981\pi$
$152$		0			0
$153$	5.56186	−	5.56186i	0.449649	−	0.449649i
$154$		0			0
$155$	0.969643	+	2.34093i	0.0778836	+	0.188028i
$156$		0			0
$157$	−16.1802	−	6.70204i	−1.29132	−	0.534881i	−0.371939	−	0.928257i	$-0.621307\pi$
$157$	−16.1802	−	6.70204i	−1.29132	−	0.534881i	−0.919378	+	0.393376i	$0.871307\pi$
$158$		0			0
$159$	0.712960			0.0565414
$160$		0			0
$161$	6.54340			0.515692
$162$		0			0
$163$	3.85564	+	1.59706i	0.301997	+	0.125091i	0.528536	−	0.848911i	$-0.322741\pi$
$163$	3.85564	+	1.59706i	0.301997	+	0.125091i	−0.226539	+	0.974002i	$0.572741\pi$
$164$		0			0
$165$	0.140553	+	0.339325i	0.0109420	+	0.0264164i
$166$		0			0
$167$	6.27859	−	6.27859i	0.485852	−	0.485852i	−0.421143	−	0.906994i	$-0.638371\pi$
$167$	6.27859	−	6.27859i	0.485852	−	0.485852i	0.906994	+	0.421143i	$0.138371\pi$
$168$		0			0
$169$	3.18124	+	3.18124i	0.244711	+	0.244711i
$170$		0			0
$171$	−19.5046	+	8.07906i	−1.49155	+	0.617821i
$172$		0			0
$173$	−5.87316	+	14.1791i	−0.446528	+	1.07801i	0.527086	+	0.849812i	$0.323285\pi$
$173$	−5.87316	+	14.1791i	−0.446528	+	1.07801i	−0.973614	+	0.228202i	$0.926715\pi$
$174$		0			0
$175$			4.92056i			0.371959i
$176$		0			0
$177$		−	3.03687i		−	0.228265i
$178$		0			0
$179$	2.67880	−	6.46719i	0.200223	−	0.483380i	−0.791594	−	0.611047i	$-0.790749\pi$
$179$	2.67880	−	6.46719i	0.200223	−	0.483380i	0.991817	+	0.127666i	$0.0407487\pi$
$180$		0			0
$181$	17.2993	−	7.16560i	1.28585	−	0.532615i	0.368101	−	0.929786i	$-0.380008\pi$
$181$	17.2993	−	7.16560i	1.28585	−	0.532615i	0.917745	+	0.397171i	$0.130008\pi$
$182$		0			0
$183$	−2.12232	−	2.12232i	−0.156886	−	0.156886i
$184$		0			0
$185$	−0.151314	+	0.151314i	−0.0111248	+	0.0111248i
$186$		0			0
$187$	−4.15796	−	10.0382i	−0.304060	−	0.734067i
$188$		0			0
$189$	1.77510	+	0.735272i	0.129120	+	0.0534832i
$190$		0			0
$191$	−19.2312			−1.39152			−0.695760	−	0.718275i	$-0.744932\pi$
$191$	−19.2312			−1.39152			−0.695760	+	0.718275i	$0.744932\pi$
$192$		0			0
$193$	14.7871			1.06440			0.532200	−	0.846619i	$-0.321366\pi$
$193$	14.7871			1.06440			0.532200	+	0.846619i	$0.321366\pi$
$194$		0			0
$195$	−0.247508	−	0.102521i	−0.0177244	−	0.00734169i
$196$		0			0
$197$	9.51406	+	22.9690i	0.677849	+	1.63647i	0.767927	+	0.640537i	$0.221288\pi$
$197$	9.51406	+	22.9690i	0.677849	+	1.63647i	−0.0900781	+	0.995935i	$0.528712\pi$
$198$		0			0
$199$	−2.37441	+	2.37441i	−0.168318	+	0.168318i	−0.786240	−	0.617922i	$-0.787975\pi$
$199$	−2.37441	+	2.37441i	−0.168318	+	0.168318i	0.617922	+	0.786240i	$0.287975\pi$
$200$		0			0
$201$	−0.0669759	−	0.0669759i	−0.00472412	−	0.00472412i
$202$		0			0
$203$	7.01178	−	2.90438i	0.492131	−	0.203847i
$204$		0			0
$205$	1.26762	−	3.06031i	0.0885344	−	0.213741i
$206$		0			0
$207$			18.9348i			1.31606i
$208$		0			0
$209$			29.1627i			2.01722i
$210$		0			0
$211$	5.26984	−	12.7225i	0.362790	−	0.875854i	−0.632099	−	0.774887i	$-0.717807\pi$
$211$	5.26984	−	12.7225i	0.362790	−	0.875854i	0.994890	−	0.100966i	$-0.0321934\pi$
$212$		0			0
$213$	−0.301566	+	0.124913i	−0.0206630	+	0.00855889i
$214$		0			0
$215$	−1.05554	−	1.05554i	−0.0719871	−	0.0719871i
$216$		0			0
$217$	6.35680	−	6.35680i	0.431528	−	0.431528i
$218$		0			0
$219$	−1.27395	−	3.07560i	−0.0860859	−	0.207830i
$220$		0			0
$221$	7.32199	+	3.03287i	0.492531	+	0.204013i
$222$		0			0
$223$	23.8616			1.59789			0.798945	−	0.601405i	$-0.205392\pi$
$223$	23.8616			1.59789			0.798945	+	0.601405i	$0.205392\pi$
$224$		0			0
$225$	−14.2387			−0.949249
$226$		0			0
$227$	−10.0398	−	4.15861i	−0.666363	−	0.276017i	0.0237501	−	0.999718i	$-0.492439\pi$
$227$	−10.0398	−	4.15861i	−0.666363	−	0.276017i	−0.690113	+	0.723701i	$0.742439\pi$
$228$		0			0
$229$	1.87824	+	4.53448i	0.124118	+	0.299647i	0.973709	−	0.227794i	$-0.0731514\pi$
$229$	1.87824	+	4.53448i	0.124118	+	0.299647i	−0.849591	+	0.527441i	$0.823151\pi$
$230$		0			0
$231$	0.921440	−	0.921440i	0.0606263	−	0.0606263i
$232$		0			0
$233$	−7.85705	−	7.85705i	−0.514733	−	0.514733i	0.401240	−	0.915973i	$-0.368579\pi$
$233$	−7.85705	−	7.85705i	−0.514733	−	0.514733i	−0.915973	+	0.401240i	$0.868579\pi$
$234$		0			0
$235$	0.786574	−	0.325810i	0.0513105	−	0.0212535i
$236$		0			0
$237$	−1.45008	+	3.50081i	−0.0941931	+	0.227402i
$238$		0			0
$239$			6.19344i			0.400620i	0.979733	+	0.200310i	$0.0641950\pi$
$239$			6.19344i			0.400620i	−0.979733	+	0.200310i	$0.935805\pi$
$240$		0			0
$241$			6.74445i			0.434448i	0.976122	+	0.217224i	$0.0697002\pi$
$241$			6.74445i			0.434448i	−0.976122	+	0.217224i	$0.930300\pi$
$242$		0			0
$243$	−3.21070	+	7.75130i	−0.205966	+	0.497246i
$244$		0			0
$245$	−0.260396	+	0.107860i	−0.0166361	+	0.00689089i
$246$		0			0
$247$	−15.0413	−	15.0413i	−0.957055	−	0.957055i
$248$		0			0
$249$	1.82064	−	1.82064i	0.115378	−	0.115378i
$250$		0			0
$251$	4.63679	+	11.1942i	0.292671	+	0.706571i	1.00000		0.000313569i	$-9.98122e-5\pi$
$251$	4.63679	+	11.1942i	0.292671	+	0.706571i	−0.707328	+	0.706885i	$0.750100\pi$
$252$		0			0
$253$	24.1647	+	10.0094i	1.51922	+	0.629283i
$254$		0			0
$255$	0.249756			0.0156403
$256$		0			0
$257$	−23.4852			−1.46496			−0.732482	−	0.680786i	$-0.761638\pi$
$257$	−23.4852			−1.46496			−0.732482	+	0.680786i	$0.761638\pi$
$258$		0			0
$259$	0.701441	+	0.290547i	0.0435854	+	0.0180537i
$260$		0			0
$261$	8.40446	+	20.2902i	0.520223	+	1.25593i
$262$		0			0
$263$	10.3745	−	10.3745i	0.639722	−	0.639722i	−0.310765	−	0.950487i	$-0.600585\pi$
$263$	10.3745	−	10.3745i	0.639722	−	0.639722i	0.950487	+	0.310765i	$0.100585\pi$
$264$		0			0
$265$	−0.435864	−	0.435864i	−0.0267749	−	0.0267749i
$266$		0			0
$267$	−1.00982	+	0.418279i	−0.0617997	+	0.0255983i
$268$		0			0
$269$	3.27890	−	7.91597i	0.199918	−	0.482645i	−0.791846	−	0.610721i	$-0.790880\pi$
$269$	3.27890	−	7.91597i	0.199918	−	0.482645i	0.991764	+	0.128075i	$0.0408799\pi$
$270$		0			0
$271$		−	23.4711i		−	1.42577i	−0.701281	−	0.712885i	$-0.747388\pi$
$271$		−	23.4711i		−	1.42577i	0.701281	−	0.712885i	$-0.252612\pi$
$272$		0			0
$273$			0.950506i			0.0575273i
$274$		0			0
$275$	−7.52692	+	18.1716i	−0.453890	+	1.09579i
$276$		0			0
$277$	2.58472	−	1.07063i	0.155301	−	0.0643276i	−0.303679	−	0.952774i	$-0.598215\pi$
$277$	2.58472	−	1.07063i	0.155301	−	0.0643276i	0.458980	+	0.888447i	$0.348215\pi$
$278$		0			0
$279$	18.3948	+	18.3948i	1.10127	+	1.10127i
$280$		0			0
$281$	11.6593	−	11.6593i	0.695538	−	0.695538i	−0.267906	−	0.963445i	$-0.586332\pi$
$281$	11.6593	−	11.6593i	0.695538	−	0.695538i	0.963445	+	0.267906i	$0.0863318\pi$
$282$		0			0
$283$	1.88336	+	4.54683i	0.111954	+	0.270281i	0.969919	−	0.243427i	$-0.0782716\pi$
$283$	1.88336	+	4.54683i	0.111954	+	0.270281i	−0.857965	+	0.513708i	$0.828272\pi$
$284$		0			0
$285$	−0.619323	−	0.256532i	−0.0366855	−	0.0151956i
$286$		0			0
$287$	−11.7525			−0.693729
$288$		0			0
$289$	9.61151			0.565383
$290$		0			0
$291$	−2.66778	−	1.10503i	−0.156388	−	0.0647780i
$292$		0			0
$293$	−4.25318	−	10.2681i	−0.248474	−	0.599869i	0.749601	−	0.661890i	$-0.230245\pi$
$293$	−4.25318	−	10.2681i	−0.248474	−	0.599869i	−0.998075	+	0.0620212i	$0.980245\pi$
$294$		0			0
$295$	−1.85657	+	1.85657i	−0.108094	+	0.108094i
$296$		0			0
$297$	5.43071	+	5.43071i	0.315122	+	0.315122i
$298$		0			0
$299$	−17.6261	+	7.30095i	−1.01934	+	0.422225i
$300$		0			0
$301$	−2.02679	+	4.89311i	−0.116822	+	0.282034i
$302$		0			0
$303$		−	0.584107i		−	0.0335561i
$304$		0			0
$305$			2.59493i			0.148585i
$306$		0			0
$307$	−2.73993	+	6.61477i	−0.156376	+	0.377525i	−0.982578	−	0.185848i	$-0.940497\pi$
$307$	−2.73993	+	6.61477i	−0.156376	+	0.377525i	0.826203	+	0.563373i	$0.190497\pi$
$308$		0			0
$309$	0.0952594	−	0.0394577i	0.00541912	−	0.00224467i
$310$		0			0
$311$	−13.0961	−	13.0961i	−0.742614	−	0.742614i	0.230466	−	0.973080i	$-0.425975\pi$
$311$	−13.0961	−	13.0961i	−0.742614	−	0.742614i	−0.973080	+	0.230466i	$0.925975\pi$
$312$		0			0
$313$	7.78991	−	7.78991i	0.440312	−	0.440312i	−0.451805	−	0.892117i	$-0.649220\pi$
$313$	7.78991	−	7.78991i	0.440312	−	0.440312i	0.892117	+	0.451805i	$0.149220\pi$
$314$		0			0
$315$	−0.312116	−	0.753514i	−0.0175857	−	0.0424557i
$316$		0			0
$317$	−7.40357	−	3.06666i	−0.415826	−	0.172241i	0.164954	−	0.986301i	$-0.447252\pi$
$317$	−7.40357	−	3.06666i	−0.415826	−	0.172241i	−0.580780	+	0.814061i	$0.697252\pi$
$318$		0			0
$319$	30.3373			1.69856
$320$		0			0
$321$	1.40989			0.0786924
$322$		0			0
$323$	18.3213	+	7.58895i	1.01943	+	0.422260i
$324$		0			0
$325$	−5.49023	−	13.2546i	−0.304543	−	0.735232i
$326$		0			0
$327$	2.98355	−	2.98355i	0.164991	−	0.164991i
$328$		0			0
$329$	−2.13595	−	2.13595i	−0.117759	−	0.117759i
$330$		0			0
$331$	−1.33540	+	0.553139i	−0.0734000	+	0.0304033i	−0.419081	−	0.907949i	$-0.637648\pi$
$331$	−1.33540	+	0.553139i	−0.0734000	+	0.0304033i	0.345681	+	0.938352i	$0.387648\pi$
$332$		0			0
$333$	−0.840761	+	2.02978i	−0.0460734	+	0.111231i
$334$		0			0
$335$			0.0818906i			0.00447416i
$336$		0			0
$337$		−	30.2285i		−	1.64665i	−0.567568	−	0.823326i	$-0.692116\pi$
$337$		−	30.2285i		−	1.64665i	0.567568	−	0.823326i	$-0.307884\pi$
$338$		0			0
$339$	−0.717904	+	1.73317i	−0.0389912	+	0.0941331i
$340$		0			0
$341$	33.1995	−	13.7517i	1.79786	−	0.744696i
$342$		0			0
$343$	0.707107	+	0.707107i	0.0381802	+	0.0381802i
$344$		0			0
$345$	−0.425134	+	0.425134i	−0.0228885	+	0.0228885i
$346$		0			0
$347$	−2.20694	−	5.32801i	−0.118475	−	0.286023i	0.853506	−	0.521082i	$-0.174472\pi$
$347$	−2.20694	−	5.32801i	−0.118475	−	0.286023i	−0.971981	+	0.235059i	$0.924472\pi$
$348$		0			0
$349$	−7.20814	−	2.98571i	−0.385843	−	0.159821i	0.181326	−	0.983423i	$-0.441961\pi$
$349$	−7.20814	−	2.98571i	−0.385843	−	0.159821i	−0.567169	+	0.823602i	$0.691961\pi$
$350$		0			0
$351$	−5.60202			−0.299014
$352$		0			0
$353$	−33.6319			−1.79004			−0.895022	−	0.446022i	$-0.852840\pi$
$353$	−33.6319			−1.79004			−0.895022	+	0.446022i	$0.852840\pi$
$354$		0			0
$355$	0.260725	+	0.107996i	0.0138379	+	0.00573183i
$356$		0			0
$357$	−0.339107	−	0.818676i	−0.0179474	−	0.0433289i
$358$		0			0
$359$	−0.146197	+	0.146197i	−0.00771599	+	0.00771599i	−0.710954	−	0.703238i	$-0.751737\pi$
$359$	−0.146197	+	0.146197i	−0.00771599	+	0.00771599i	0.703238	+	0.710954i	$0.251737\pi$
$360$		0			0
$361$	−24.2018	−	24.2018i	−1.27378	−	1.27378i
$362$		0			0
$363$	1.49935	−	0.621049i	0.0786952	−	0.0325966i
$364$		0			0
$365$	−1.10142	+	2.65907i	−0.0576511	+	0.139182i
$366$		0			0
$367$		−	15.1328i		−	0.789925i	−0.918697	−	0.394963i	$-0.870758\pi$
$367$		−	15.1328i		−	0.789925i	0.918697	−	0.394963i	$-0.129242\pi$
$368$		0			0
$369$		−	34.0085i		−	1.77041i
$370$		0			0
$371$	−0.836925	+	2.02051i	−0.0434510	+	0.104900i
$372$		0			0
$373$	−29.9350	+	12.3995i	−1.54998	+	0.642021i	−0.983312	−	0.181929i	$-0.941766\pi$
$373$	−29.9350	+	12.3995i	−1.54998	+	0.642021i	−0.566663	+	0.823949i	$0.691766\pi$
$374$		0			0
$375$	−0.644553	−	0.644553i	−0.0332846	−	0.0332846i
$376$		0			0
$377$	−15.6471	+	15.6471i	−0.805868	+	0.805868i
$378$		0			0
$379$	2.98517	+	7.20685i	0.153338	+	0.370191i	0.981817	−	0.189829i	$-0.0607934\pi$
$379$	2.98517	+	7.20685i	0.153338	+	0.370191i	−0.828479	+	0.560020i	$0.810793\pi$
$380$		0			0
$381$	2.55431	+	1.05803i	0.130861	+	0.0542045i
$382$		0			0
$383$	−11.0595			−0.565112			−0.282556	−	0.959251i	$-0.591182\pi$
$383$	−11.0595			−0.565112			−0.282556	+	0.959251i	$0.591182\pi$
$384$		0			0
$385$	−1.12663			−0.0574185
$386$		0			0
$387$	−14.1593	−	5.86498i	−0.719759	−	0.298134i
$388$		0			0
$389$	3.55159	+	8.57429i	0.180073	+	0.434734i	0.987981	−	0.154574i	$-0.0494005\pi$
$389$	3.55159	+	8.57429i	0.180073	+	0.434734i	−0.807909	+	0.589308i	$0.799401\pi$
$390$		0			0
$391$	12.5767	−	12.5767i	0.636031	−	0.636031i
$392$		0			0
$393$	4.52377	+	4.52377i	0.228194	+	0.228194i
$394$		0			0
$395$	3.02670	−	1.25370i	0.152290	−	0.0630804i
$396$		0			0
$397$	−10.6583	+	25.7314i	−0.534924	+	1.29142i	0.393304	+	0.919408i	$0.371332\pi$
$397$	−10.6583	+	25.7314i	−0.534924	+	1.29142i	−0.928228	+	0.372012i	$0.878668\pi$
$398$		0			0
$399$			2.37839i			0.119068i
$400$		0			0
$401$			4.20855i			0.210165i	0.994464	+	0.105082i	$0.0335106\pi$
$401$			4.20855i			0.210165i	−0.994464	+	0.105082i	$0.966489\pi$
$402$		0			0
$403$	−10.0307	+	24.2161i	−0.499663	+	1.20629i
$404$		0			0
$405$	2.09744	−	0.868788i	0.104223	−	0.0431704i
$406$		0			0
$407$	2.14597	+	2.14597i	0.106372	+	0.106372i
$408$		0			0
$409$	−5.37660	+	5.37660i	−0.265856	+	0.265856i	−0.827428	−	0.561572i	$-0.810197\pi$
$409$	−5.37660	+	5.37660i	−0.265856	+	0.265856i	0.561572	+	0.827428i	$0.310197\pi$
$410$		0			0
$411$	1.80809	+	4.36511i	0.0891864	+	0.215315i
$412$		0			0
$413$	8.60644	+	3.56490i	0.423495	+	0.175417i
$414$		0			0
$415$	−2.22607			−0.109273
$416$		0			0
$417$	−4.51992			−0.221341
$418$		0			0
$419$	−2.50381	−	1.03711i	−0.122319	−	0.0506663i	0.320684	−	0.947186i	$-0.396087\pi$
$419$	−2.50381	−	1.03711i	−0.122319	−	0.0506663i	−0.443004	+	0.896520i	$0.646087\pi$
$420$		0			0
$421$	−4.95708	−	11.9675i	−0.241594	−	0.583258i	0.755848	−	0.654747i	$-0.227225\pi$
$421$	−4.95708	−	11.9675i	−0.241594	−	0.583258i	−0.997441	+	0.0714889i	$0.977225\pi$
$422$		0			0
$423$	6.18084	−	6.18084i	0.300523	−	0.300523i
$424$		0			0
$425$	9.45752	+	9.45752i	0.458757	+	0.458757i
$426$		0			0
$427$	8.50594	−	3.52327i	0.411631	−	0.170503i
$428$		0			0
$429$	−1.45398	+	3.51021i	−0.0701987	+	0.169475i
$430$		0			0
$431$			12.0032i			0.578172i	0.957303	+	0.289086i	$0.0933514\pi$
$431$			12.0032i			0.578172i	−0.957303	+	0.289086i	$0.906649\pi$
$432$		0			0
$433$		−	22.9692i		−	1.10383i	−0.833900	−	0.551915i	$-0.813897\pi$
$433$		−	22.9692i		−	1.10383i	0.833900	−	0.551915i	$-0.186103\pi$
$434$		0			0
$435$	−0.266864	+	0.644267i	−0.0127952	+	0.0308903i
$436$		0			0
$437$	−44.1045	+	18.2687i	−2.10980	+	0.873910i
$438$		0			0
$439$	6.27527	+	6.27527i	0.299502	+	0.299502i	0.840819	−	0.541317i	$-0.182074\pi$
$439$	6.27527	+	6.27527i	0.299502	+	0.299502i	−0.541317	+	0.840819i	$0.682074\pi$
$440$		0			0
$441$	−2.04617	+	2.04617i	−0.0974367	+	0.0974367i
$442$		0			0
$443$	2.49198	+	6.01618i	0.118398	+	0.285837i	0.971957	−	0.235158i	$-0.0755609\pi$
$443$	2.49198	+	6.01618i	0.118398	+	0.285837i	−0.853559	+	0.520995i	$0.825561\pi$
$444$		0			0
$445$	0.873056	+	0.361632i	0.0413868	+	0.0171430i
$446$		0			0
$447$	0.873745			0.0413267
$448$		0			0
$449$	27.1735			1.28239			0.641197	−	0.767376i	$-0.278438\pi$
$449$	27.1735			1.28239			0.641197	+	0.767376i	$0.278438\pi$
$450$		0			0
$451$	−43.4019	−	17.9777i	−2.04372	−	0.846535i
$452$		0			0
$453$	0.183084	+	0.442003i	0.00860202	+	0.0207671i
$454$		0			0
$455$	0.581086	−	0.581086i	0.0272417	−	0.0272417i
$456$		0			0
$457$	−22.5421	−	22.5421i	−1.05447	−	1.05447i	−0.998428	−	0.0560450i	$-0.982151\pi$
$457$	−22.5421	−	22.5421i	−1.05447	−	1.05447i	−0.0560450	−	0.998428i	$-0.517849\pi$
$458$		0			0
$459$	4.82505	−	1.99860i	0.225214	−	0.0932867i
$460$		0			0
$461$	15.4099	−	37.2027i	0.717709	−	1.73270i	0.0379346	−	0.999280i	$-0.487922\pi$
$461$	15.4099	−	37.2027i	0.717709	−	1.73270i	0.679774	−	0.733422i	$-0.262078\pi$
$462$		0			0
$463$		−	37.4906i		−	1.74234i	−0.490984	−	0.871168i	$-0.663363\pi$
$463$		−	37.4906i		−	1.74234i	0.490984	−	0.871168i	$-0.336637\pi$
$464$		0			0
$465$			0.826021i			0.0383058i
$466$		0			0
$467$	9.47715	−	22.8799i	0.438550	−	1.05875i	−0.537900	−	0.843009i	$-0.680782\pi$
$467$	9.47715	−	22.8799i	0.438550	−	1.05875i	0.976450	−	0.215745i	$-0.0692179\pi$
$468$		0			0
$469$	0.268430	−	0.111187i	0.0123949	−	0.00513415i
$470$		0			0
$471$	−4.03712	−	4.03712i	−0.186020	−	0.186020i
$472$		0			0
$473$	−14.9699	+	14.9699i	−0.688315	+	0.688315i
$474$		0			0
$475$	−13.7378	−	33.1661i	−0.630335	−	1.52176i
$476$		0			0
$477$	−5.84681	−	2.42183i	−0.267707	−	0.110888i
$478$		0			0
$479$	20.5038			0.936844			0.468422	−	0.883505i	$-0.344823\pi$
$479$	20.5038			0.936844			0.468422	+	0.883505i	$0.344823\pi$
$480$		0			0
$481$	−2.21367			−0.100935
$482$		0			0
$483$	1.97078	+	0.816323i	0.0896735	+	0.0371440i
$484$		0			0
$485$	0.955376	+	2.30648i	0.0433814	+	0.104732i
$486$		0			0
$487$	13.7573	−	13.7573i	0.623401	−	0.623401i	−0.322998	−	0.946399i	$-0.604691\pi$
$487$	13.7573	−	13.7573i	0.623401	−	0.623401i	0.946399	+	0.322998i	$0.104691\pi$
$488$		0			0
$489$	0.962022	+	0.962022i	0.0435041	+	0.0435041i
$490$		0			0
$491$	−4.31959	+	1.78923i	−0.194940	+	0.0807469i	−0.478018	−	0.878350i	$-0.658645\pi$
$491$	−4.31959	+	1.78923i	−0.194940	+	0.0807469i	0.283078	+	0.959097i	$0.408645\pi$
$492$		0			0
$493$	7.89461	−	19.0593i	0.355555	−	0.858386i
$494$		0			0
$495$		−	3.26016i		−	0.146533i
$496$		0			0
$497$		−	1.00126i		−	0.0449129i
$498$		0			0
$499$	15.7069	−	37.9199i	0.703140	−	1.69753i	−0.0133304	−	0.999911i	$-0.504243\pi$
$499$	15.7069	−	37.9199i	0.703140	−	1.69753i	0.716470	−	0.697618i	$-0.245757\pi$
$500$		0			0
$501$	2.67431	−	1.10773i	0.119479	−	0.0494899i
$502$		0			0
$503$	11.6209	+	11.6209i	0.518150	+	0.518150i	0.917011	−	0.398862i	$-0.130595\pi$
$503$	11.6209	+	11.6209i	0.518150	+	0.518150i	−0.398862	+	0.917011i	$0.630595\pi$
$504$		0			0
$505$	−0.357090	+	0.357090i	−0.0158903	+	0.0158903i
$506$		0			0
$507$	0.561267	+	1.35502i	0.0249268	+	0.0601785i
$508$		0			0
$509$	−9.58321	−	3.96950i	−0.424768	−	0.175945i	0.160050	−	0.987109i	$-0.448834\pi$
$509$	−9.58321	−	3.96950i	−0.424768	−	0.175945i	−0.584819	+	0.811164i	$0.698834\pi$
$510$		0			0
$511$	10.2116			0.451736
$512$		0			0
$513$	−14.0176			−0.618891
$514$		0			0
$515$	−0.0823584	−	0.0341140i	−0.00362915	−	0.00150324i
$516$		0			0
$517$	−4.62071	−	11.1554i	−0.203218	−	0.490613i
$518$		0			0
$519$	−3.53782	+	3.53782i	−0.155293	+	0.155293i
$520$		0			0
$521$	−16.2077	−	16.2077i	−0.710072	−	0.710072i	0.256478	−	0.966550i	$-0.417438\pi$
$521$	−16.2077	−	16.2077i	−0.710072	−	0.710072i	−0.966550	+	0.256478i	$0.917438\pi$
$522$		0			0
$523$	−12.5812	+	5.21130i	−0.550137	+	0.227874i	−0.640397	−	0.768044i	$-0.721230\pi$
$523$	−12.5812	+	5.21130i	−0.550137	+	0.227874i	0.0902602	+	0.995918i	$0.471230\pi$
$524$		0			0
$525$	−0.613865	+	1.48200i	−0.0267913	+	0.0646799i
$526$		0			0
$527$		−	24.4361i		−	1.06445i
$528$		0			0
$529$			19.8161i			0.861570i
$530$		0			0
$531$	−10.3158	+	24.9046i	−0.447669	+	1.08077i
$532$		0			0
$533$	31.6579	−	13.1131i	1.37126	−	0.567993i
$534$		0			0
$535$	−0.861927	−	0.861927i	−0.0372643	−	0.0372643i
$536$		0			0
$537$	1.61363	−	1.61363i	0.0696333	−	0.0696333i
$538$		0			0
$539$	1.52969	+	3.69299i	0.0658883	+	0.159068i
$540$		0			0
$541$	37.0570	+	15.3495i	1.59321	+	0.659928i	0.990434	−	0.137986i	$-0.0440629\pi$
$541$	37.0570	+	15.3495i	1.59321	+	0.659928i	0.602772	+	0.797914i	$0.294063\pi$
$542$		0			0
$543$	6.10424			0.261958
$544$		0			0
$545$	−3.64794			−0.156261
$546$		0			0
$547$	17.9751	+	7.44554i	0.768561	+	0.318348i	0.732289	−	0.680994i	$-0.238452\pi$
$547$	17.9751	+	7.44554i	0.768561	+	0.318348i	0.0362713	+	0.999342i	$0.488452\pi$
$548$		0			0
$549$	10.1954	+	24.6138i	0.435128	+	1.05049i
$550$		0			0
$551$	−39.1527	+	39.1527i	−1.66796	+	1.66796i
$552$		0			0
$553$	−8.21901	−	8.21901i	−0.349508	−	0.349508i
$554$		0			0
$555$	−0.0644509	+	0.0266964i	−0.00273579	+	0.00113320i
$556$		0			0
$557$	11.1741	−	26.9767i	0.473462	−	1.14304i	−0.489161	−	0.872193i	$-0.662697\pi$
$557$	11.1741	−	26.9767i	0.473462	−	1.14304i	0.962623	−	0.270845i	$-0.0873030\pi$
$558$		0			0
$559$		−	15.4421i		−	0.653131i
$560$		0			0
$561$		−	3.54209i		−	0.149547i
$562$		0			0
$563$	−7.04007	+	16.9962i	−0.296703	+	0.716305i	0.703282	+	0.710911i	$0.251717\pi$
$563$	−7.04007	+	16.9962i	−0.296703	+	0.716305i	−0.999985	+	0.00539444i	$0.998283\pi$
$564$		0			0
$565$	1.49845	−	0.620679i	0.0630403	−	0.0261121i
$566$		0			0
$567$	−5.69561	−	5.69561i	−0.239193	−	0.239193i
$568$		0			0
$569$	8.98613	−	8.98613i	0.376718	−	0.376718i	−0.493199	−	0.869917i	$-0.664172\pi$
$569$	8.98613	−	8.98613i	0.376718	−	0.376718i	0.869917	+	0.493199i	$0.164172\pi$
$570$		0			0
$571$	−2.59176	−	6.25707i	−0.108462	−	0.261850i	0.860325	−	0.509746i	$-0.170261\pi$
$571$	−2.59176	−	6.25707i	−0.108462	−	0.261850i	−0.968787	+	0.247896i	$0.920261\pi$
$572$		0			0
$573$	−5.79215	−	2.39919i	−0.241971	−	0.100228i
$574$		0			0
$575$	−32.1972			−1.34272
$576$		0			0
$577$	17.5809			0.731904			0.365952	−	0.930634i	$-0.380743\pi$
$577$	17.5809			0.731904			0.365952	+	0.930634i	$0.380743\pi$
$578$		0			0
$579$	4.45366	+	1.84477i	0.185088	+	0.0766659i
$580$		0			0
$581$	3.02245	+	7.29684i	0.125392	+	0.302724i
$582$		0			0
$583$	−6.18151	+	6.18151i	−0.256012	+	0.256012i
$584$		0			0
$585$	1.68150	+	1.68150i	0.0695215	+	0.0695215i
$586$		0			0
$587$	−33.5468	+	13.8955i	−1.38462	+	0.573530i	−0.945713	−	0.325002i	$-0.894635\pi$
$587$	−33.5468	+	13.8955i	−1.38462	+	0.573530i	−0.438910	+	0.898531i	$0.644635\pi$
$588$		0			0
$589$	−25.0990	+	60.5944i	−1.03419	+	2.49675i
$590$		0			0
$591$			8.10485i			0.333389i
$592$		0			0
$593$		−	13.3080i		−	0.546493i	−0.961944	−	0.273246i	$-0.911903\pi$
$593$		−	13.3080i		−	0.546493i	0.961944	−	0.273246i	$-0.0880975\pi$
$594$		0			0
$595$	−0.293181	+	0.707802i	−0.0120193	+	0.0290171i
$596$		0			0
$597$	−1.01136	+	0.418919i	−0.0413922	+	0.0171452i
$598$		0			0
$599$	−8.04219	−	8.04219i	−0.328595	−	0.328595i	0.523457	−	0.852052i	$-0.324642\pi$
$599$	−8.04219	−	8.04219i	−0.328595	−	0.328595i	−0.852052	+	0.523457i	$0.824642\pi$
$600$		0			0
$601$	−18.9773	+	18.9773i	−0.774099	+	0.774099i	−0.978820	−	0.204721i	$-0.934371\pi$
$601$	−18.9773	+	18.9773i	−0.774099	+	0.774099i	0.204721	+	0.978820i	$0.434371\pi$
$602$		0			0
$603$	0.321745	+	0.776761i	0.0131025	+	0.0316322i
$604$		0			0
$605$	−1.29629	−	0.536940i	−0.0527016	−	0.0218297i
$606$		0			0
$607$	−26.5677			−1.07835			−0.539175	−	0.842194i	$-0.681264\pi$
$607$	−26.5677			−1.07835			−0.539175	+	0.842194i	$0.681264\pi$
$608$		0			0
$609$	2.47418			0.100259
$610$		0			0
$611$	8.13687	+	3.37040i	0.329182	+	0.136352i
$612$		0			0
$613$	−11.6096	−	28.0281i	−0.468907	−	1.13204i	−0.964641	−	0.263568i	$-0.915101\pi$
$613$	−11.6096	−	28.0281i	−0.468907	−	1.13204i	0.495734	−	0.868475i	$-0.334899\pi$
$614$		0			0
$615$	0.763578	−	0.763578i	0.0307904	−	0.0307904i
$616$		0			0
$617$	−8.41445	−	8.41445i	−0.338753	−	0.338753i	0.517145	−	0.855898i	$-0.326995\pi$
$617$	−8.41445	−	8.41445i	−0.338753	−	0.338753i	−0.855898	+	0.517145i	$0.826995\pi$
$618$		0			0
$619$	33.2087	−	13.7555i	1.33477	−	0.552879i	0.402757	−	0.915307i	$-0.368052\pi$
$619$	33.2087	−	13.7555i	1.33477	−	0.552879i	0.932012	+	0.362428i	$0.118052\pi$
$620$		0			0
$621$	−4.81118	+	11.6152i	−0.193066	+	0.466103i
$622$		0			0
$623$		−	3.35280i		−	0.134327i
$624$		0			0
$625$		−	23.8147i		−	0.952589i
$626$		0			0
$627$	−3.63819	+	8.78337i	−0.145295	+	0.350774i
$628$		0			0
$629$	1.90664	−	0.789757i	0.0760228	−	0.0314897i
$630$		0			0
$631$	21.9924	+	21.9924i	0.875503	+	0.875503i	0.993065	−	0.117563i	$-0.0375081\pi$
$631$	21.9924	+	21.9924i	0.875503	+	0.875503i	−0.117563	+	0.993065i	$0.537508\pi$
$632$		0			0
$633$	3.17440	−	3.17440i	0.126171	−	0.126171i
$634$		0			0
$635$	−0.914740	−	2.20838i	−0.0363004	−	0.0876368i
$636$		0			0
$637$	−2.69371	−	1.11577i	−0.106729	−	0.0442085i
$638$		0			0
$639$	2.89738			0.114619
$640$		0			0
$641$	37.6306			1.48632			0.743161	−	0.669113i	$-0.233326\pi$
$641$	37.6306			1.48632			0.743161	+	0.669113i	$0.233326\pi$
$642$		0			0
$643$	−42.1313	−	17.4513i	−1.66150	−	0.688214i	−0.663305	−	0.748349i	$-0.730847\pi$
$643$	−42.1313	−	17.4513i	−1.66150	−	0.688214i	−0.998190	+	0.0601352i	$0.980847\pi$
$644$		0			0
$645$	−0.186229	−	0.449597i	−0.00733276	−	0.0177028i
$646$		0			0
$647$	−1.93803	+	1.93803i	−0.0761917	+	0.0761917i	−0.744176	−	0.667984i	$-0.767157\pi$
$647$	−1.93803	+	1.93803i	−0.0761917	+	0.0761917i	0.667984	+	0.744176i	$0.267157\pi$
$648$		0			0
$649$	26.3303	+	26.3303i	1.03356	+	1.03356i
$650$		0			0
$651$	2.70762	−	1.12153i	0.106120	−	0.0439563i
$652$		0			0
$653$	−2.14157	+	5.17021i	−0.0838061	+	0.202326i	−0.960227	−	0.279219i	$-0.909924\pi$
$653$	−2.14157	+	5.17021i	−0.0838061	+	0.202326i	0.876421	+	0.481545i	$0.159924\pi$
$654$		0			0
$655$		−	5.53115i		−	0.216120i
$656$		0			0
$657$			29.5497i			1.15284i
$658$		0			0
$659$	−1.59823	+	3.85847i	−0.0622583	+	0.150305i	−0.951947	−	0.306263i	$-0.900921\pi$
$659$	−1.59823	+	3.85847i	−0.0622583	+	0.150305i	0.889689	+	0.456568i	$0.150921\pi$
$660$		0			0
$661$	25.3284	−	10.4914i	0.985162	−	0.408068i	0.168827	−	0.985646i	$-0.446002\pi$
$661$	25.3284	−	10.4914i	0.985162	−	0.408068i	0.816335	+	0.577578i	$0.196002\pi$
$662$		0			0
$663$	1.82691	+	1.82691i	0.0709514	+	0.0709514i
$664$		0			0
$665$	1.45401	−	1.45401i	0.0563842	−	0.0563842i
$666$		0			0
$667$	19.0045	+	45.8809i	0.735857	+	1.77652i
$668$		0			0
$669$	7.18676	+	2.97685i	0.277856	+	0.115092i
$670$		0			0
$671$	36.8019			1.42072
$672$		0			0
$673$	−6.40774			−0.247000			−0.123500	−	0.992345i	$-0.539412\pi$
$673$	−6.40774			−0.247000			−0.123500	+	0.992345i	$0.539412\pi$
$674$		0			0
$675$	−8.73451	−	3.61795i	−0.336191	−	0.139255i
$676$		0			0
$677$	−18.5720	−	44.8368i	−0.713780	−	1.72322i	−0.690331	−	0.723493i	$-0.742535\pi$
$677$	−18.5720	−	44.8368i	−0.713780	−	1.72322i	−0.0234490	−	0.999725i	$-0.507465\pi$
$678$		0			0
$679$	6.26326	−	6.26326i	0.240362	−	0.240362i
$680$		0			0
$681$	−2.50503	−	2.50503i	−0.0959928	−	0.0959928i
$682$		0			0
$683$	38.9317	−	16.1260i	1.48968	−	0.617045i	0.518431	−	0.855119i	$-0.326516\pi$
$683$	38.9317	−	16.1260i	1.48968	−	0.617045i	0.971247	+	0.238074i	$0.0765162\pi$
$684$		0			0
$685$	1.56322	−	3.77394i	0.0597275	−	0.144195i
$686$		0			0
$687$			1.60004i			0.0610454i
$688$		0			0
$689$		−	6.37651i		−	0.242926i
$690$		0			0
$691$	2.18633	−	5.27826i	0.0831718	−	0.200795i	−0.876822	−	0.480814i	$-0.840341\pi$
$691$	2.18633	−	5.27826i	0.0831718	−	0.200795i	0.959994	+	0.280020i	$0.0903411\pi$
$692$		0			0
$693$	−10.6865	+	4.42649i	−0.405947	+	0.168149i
$694$		0			0
$695$	2.76322	+	2.76322i	0.104815	+	0.104815i
$696$		0			0
$697$	−22.5888	+	22.5888i	−0.855612	+	0.855612i
$698$		0			0
$699$	−1.38622	−	3.34664i	−0.0524318	−	0.126581i
$700$		0			0
$701$	−6.12292	−	2.53620i	−0.231259	−	0.0957908i	0.264045	−	0.964510i	$-0.414943\pi$
$701$	−6.12292	−	2.53620i	−0.231259	−	0.0957908i	−0.495304	+	0.868720i	$0.664943\pi$
$702$		0			0
$703$	−5.53911			−0.208912
$704$		0			0
$705$	0.277551			0.0104532
$706$		0			0
$707$	1.65535	+	0.685667i	0.0622557	+	0.0257872i
$708$		0			0
$709$	0.334454	+	0.807444i	0.0125607	+	0.0303242i	0.930035	−	0.367470i	$-0.119776\pi$
$709$	0.334454	+	0.807444i	0.0125607	+	0.0303242i	−0.917475	+	0.397794i	$0.869776\pi$
$710$		0			0
$711$	23.7836	−	23.7836i	0.891953	−	0.891953i
$712$		0			0
$713$	41.5951	+	41.5951i	1.55775	+	1.55775i
$714$		0			0
$715$	3.03482	−	1.25707i	0.113496	−	0.0470116i
$716$		0			0
$717$	−0.772664	+	1.86537i	−0.0288556	+	0.0696637i
$718$		0			0
$719$		−	14.0156i		−	0.522693i	−0.965245	−	0.261346i	$-0.915833\pi$
$719$		−	14.0156i		−	0.522693i	0.965245	−	0.261346i	$-0.0841665\pi$
$720$		0			0
$721$			0.316281i			0.0117789i
$722$		0			0
$723$	−0.841404	+	2.03133i	−0.0312922	+	0.0755460i
$724$		0			0
$725$	−34.5019	+	14.2912i	−1.28137	+	0.530760i
$726$		0			0
$727$	−6.72385	−	6.72385i	−0.249374	−	0.249374i	0.571340	−	0.820714i	$-0.306424\pi$
$727$	−6.72385	−	6.72385i	−0.249374	−	0.249374i	−0.820714	+	0.571340i	$0.806424\pi$
$728$		0			0
$729$	15.1528	−	15.1528i	0.561215	−	0.561215i
$730$		0			0
$731$	5.50919	+	13.3003i	0.203765	+	0.491931i
$732$		0			0
$733$	35.3811	+	14.6553i	1.30683	+	0.541307i	0.923958	−	0.382494i	$-0.124935\pi$
$733$	35.3811	+	14.6553i	1.30683	+	0.541307i	0.382873	+	0.923801i	$0.374935\pi$
$734$		0			0
$735$	−0.0918835			−0.00338917
$736$		0			0
$737$	1.16139			0.0427804
$738$		0			0
$739$	−48.0011	−	19.8827i	−1.76575	−	0.731397i	−0.995618	−	0.0935103i	$-0.970191\pi$
$739$	−48.0011	−	19.8827i	−1.76575	−	0.731397i	−0.770130	−	0.637887i	$-0.779809\pi$
$740$		0			0
$741$	−2.65374	−	6.40670i	−0.0974876	−	0.235356i
$742$		0			0
$743$	−18.5412	+	18.5412i	−0.680210	+	0.680210i	−0.960047	−	0.279837i	$-0.909719\pi$
$743$	−18.5412	+	18.5412i	−0.680210	+	0.680210i	0.279837	+	0.960047i	$0.409719\pi$
$744$		0			0
$745$	−0.534158	−	0.534158i	−0.0195700	−	0.0195700i
$746$		0			0
$747$	−21.1150	+	8.74613i	−0.772559	+	0.320004i
$748$		0			0
$749$	−1.65503	+	3.99560i	−0.0604735	+	0.145996i
$750$		0			0
$751$			45.4645i			1.65902i	0.558489	+	0.829512i	$0.311381\pi$
$751$			45.4645i			1.65902i	−0.558489	+	0.829512i	$0.688619\pi$
$752$		0			0
$753$			3.94999i			0.143946i
$754$		0			0
$755$	0.158289	−	0.382143i	0.00576071	−	0.0139076i
$756$		0			0
$757$	5.36088	−	2.22055i	0.194844	−	0.0807072i	−0.283128	−	0.959082i	$-0.591372\pi$
$757$	5.36088	−	2.22055i	0.194844	−	0.0807072i	0.477972	+	0.878375i	$0.341372\pi$
$758$		0			0
$759$	6.02935	+	6.02935i	0.218852	+	0.218852i
$760$		0			0
$761$	7.34122	−	7.34122i	0.266119	−	0.266119i	−0.561415	−	0.827534i	$-0.689743\pi$
$761$	7.34122	−	7.34122i	0.266119	−	0.266119i	0.827534	+	0.561415i	$0.189743\pi$
$762$		0			0
$763$	4.95301	+	11.9576i	0.179311	+	0.432895i
$764$		0			0
$765$	−2.04818	−	0.848386i	−0.0740523	−	0.0306734i
$766$		0			0
$767$	−27.1609			−0.980724
$768$		0			0
$769$	43.4536			1.56698			0.783489	−	0.621406i	$-0.213438\pi$
$769$	43.4536			1.56698			0.783489	+	0.621406i	$0.213438\pi$
$770$		0			0
$771$	−7.07339	−	2.92989i	−0.254742	−	0.105518i
$772$		0			0
$773$	−1.73290	−	4.18358i	−0.0623279	−	0.150473i	0.889647	−	0.456649i	$-0.150950\pi$
$773$	−1.73290	−	4.18358i	−0.0623279	−	0.150473i	−0.951975	+	0.306176i	$0.900950\pi$
$774$		0			0
$775$	−31.2790	+	31.2790i	−1.12358	+	1.12358i
$776$		0			0
$777$	0.175017	+	0.175017i	0.00627869	+	0.00627869i
$778$		0			0
$779$	79.2155	−	32.8121i	2.83819	−	1.17562i
$780$		0			0
$781$	1.53162	−	3.69766i	0.0548058	−	0.132313i
$782$		0			0
$783$			14.5822i			0.521124i
$784$		0			0
$785$			4.93613i			0.176178i
$786$		0			0
$787$	2.59802	−	6.27218i	0.0926095	−	0.223579i	−0.870787	−	0.491661i	$-0.836390\pi$
$787$	2.59802	−	6.27218i	0.0926095	−	0.223579i	0.963396	+	0.268082i	$0.0863899\pi$
$788$		0			0
$789$	4.41894	−	1.83038i	0.157318	−	0.0651634i
$790$		0			0
$791$	−4.06905	−	4.06905i	−0.144679	−	0.144679i
$792$		0			0
$793$	−18.9814	+	18.9814i	−0.674049	+	0.674049i
$794$		0			0
$795$	−0.0768996	−	0.185652i	−0.00272735	−	0.00658440i
$796$		0			0
$797$	20.2307	+	8.37983i	0.716608	+	0.296829i	0.711036	−	0.703156i	$-0.248226\pi$
$797$	20.2307	+	8.37983i	0.716608	+	0.296829i	0.00557212	+	0.999984i	$0.498226\pi$
$798$		0			0
$799$	−8.21076			−0.290476
$800$		0			0
$801$	9.70208			0.342806
$802$		0			0
$803$	37.7115	+	15.6206i	1.33081	+	0.551240i
$804$		0			0
$805$	−0.705768	−	1.70388i	−0.0248751	−	0.0600537i
$806$		0			0
$807$	1.97512	−	1.97512i	0.0695274	−	0.0695274i
$808$		0			0
$809$	10.2533	+	10.2533i	0.360488	+	0.360488i	0.863993	−	0.503504i	$-0.167956\pi$
$809$	10.2533	+	10.2533i	0.360488	+	0.360488i	−0.503504	+	0.863993i	$0.667956\pi$
$810$		0			0
$811$	9.24624	−	3.82992i	0.324679	−	0.134487i	−0.214390	−	0.976748i	$-0.568776\pi$
$811$	9.24624	−	3.82992i	0.324679	−	0.134487i	0.539069	+	0.842262i	$0.318776\pi$
$812$		0			0
$813$	2.92814	−	7.06916i	0.102694	−	0.247926i
$814$		0			0
$815$		−	1.17625i		−	0.0412023i
$816$		0			0
$817$		−	38.6397i		−	1.35183i
$818$		0			0
$819$	3.22874	−	7.79487i	0.112821	−	0.272375i
$820$		0			0
$821$	−42.6045	+	17.6474i	−1.48691	+	0.615897i	−0.970641	−	0.240532i	$-0.922678\pi$
$821$	−42.6045	+	17.6474i	−1.48691	+	0.615897i	−0.516265	+	0.856429i	$0.672678\pi$
$822$		0			0
$823$	18.0227	+	18.0227i	0.628232	+	0.628232i	0.947623	−	0.319391i	$-0.103478\pi$
$823$	18.0227	+	18.0227i	0.628232	+	0.628232i	−0.319391	+	0.947623i	$0.603478\pi$
$824$		0			0
$825$	−4.53400	+	4.53400i	−0.157854	+	0.157854i
$826$		0			0
$827$	−12.3339	−	29.7767i	−0.428893	−	1.03544i	−0.979639	−	0.200766i	$-0.935657\pi$
$827$	−12.3339	−	29.7767i	−0.428893	−	1.03544i	0.550746	−	0.834673i	$-0.314343\pi$
$828$		0			0
$829$	13.3318	+	5.52220i	0.463032	+	0.191794i	0.601989	−	0.798504i	$-0.294375\pi$
$829$	13.3318	+	5.52220i	0.463032	+	0.191794i	−0.138957	+	0.990298i	$0.544375\pi$
$830$		0			0
$831$	0.912046			0.0316385
$832$		0			0
$833$	2.71818			0.0941793
$834$		0			0
$835$	−2.31213	−	0.957714i	−0.0800144	−	0.0331431i
$836$		0			0
$837$	6.61000	+	15.9580i	0.228475	+	0.551588i
$838$		0			0
$839$	−22.5152	+	22.5152i	−0.777312	+	0.777312i	−0.979373	−	0.202061i	$-0.935236\pi$
$839$	−22.5152	+	22.5152i	−0.777312	+	0.777312i	0.202061	+	0.979373i	$0.435236\pi$
$840$		0			0
$841$	20.2236	+	20.2236i	0.697366	+	0.697366i
$842$		0			0
$843$	4.96619	−	2.05706i	0.171045	−	0.0708490i
$844$		0			0
$845$	0.485255	−	1.17151i	0.0166933	−	0.0403011i
$846$		0			0
$847$			4.97814i			0.171051i
$848$		0			0
$849$			1.60440i			0.0550628i
$850$		0			0
$851$	−1.90116	+	4.58981i	−0.0651710	+	0.157337i
$852$		0			0
$853$	12.9659	−	5.37067i	0.443946	−	0.183888i	−0.149501	−	0.988762i	$-0.547767\pi$
$853$	12.9659	−	5.37067i	0.443946	−	0.183888i	0.593447	+	0.804873i	$0.297767\pi$
$854$		0			0
$855$	4.20751	+	4.20751i	0.143894	+	0.143894i
$856$		0			0
$857$	−35.2880	+	35.2880i	−1.20541	+	1.20541i	−0.232917	+	0.972497i	$0.574827\pi$
$857$	−35.2880	+	35.2880i	−1.20541	+	1.20541i	−0.972497	+	0.232917i	$0.925173\pi$
$858$		0			0
$859$	5.84350	+	14.1075i	0.199378	+	0.481341i	0.991671	−	0.128801i	$-0.0411127\pi$
$859$	5.84350	+	14.1075i	0.199378	+	0.481341i	−0.792293	+	0.610141i	$0.791113\pi$
$860$		0			0
$861$	−3.53969	−	1.46619i	−0.120632	−	0.0499675i
$862$		0			0
$863$	−21.1570			−0.720191			−0.360095	−	0.932915i	$-0.617256\pi$
$863$	−21.1570			−0.720191			−0.360095	+	0.932915i	$0.617256\pi$
$864$		0			0
$865$	4.32565			0.147076
$866$		0			0
$867$	2.89485	+	1.19909i	0.0983142	+	0.0407231i
$868$		0			0
$869$	−17.7802	−	42.9253i	−0.603153	−	1.45614i
$870$		0			0
$871$	−0.599013	+	0.599013i	−0.0202968	+	0.0202968i
$872$		0			0
$873$	18.1242	+	18.1242i	0.613410	+	0.613410i
$874$		0			0
$875$	2.58327	−	1.07003i	0.0873306	−	0.0361735i
$876$		0			0
$877$	−2.32861	+	5.62176i	−0.0786315	+	0.189833i	−0.958307	−	0.285742i	$-0.907760\pi$
$877$	−2.32861	+	5.62176i	−0.0786315	+	0.189833i	0.879675	+	0.475575i	$0.157760\pi$
$878$		0			0
$879$		−	3.62321i		−	0.122208i
$880$		0			0
$881$			3.59365i			0.121073i	0.998166	+	0.0605366i	$0.0192812\pi$
$881$			3.59365i			0.121073i	−0.998166	+	0.0605366i	$0.980719\pi$
$882$		0			0
$883$	−2.30910	+	5.57466i	−0.0777074	+	0.187602i	−0.957959	−	0.286905i	$-0.907374\pi$
$883$	−2.30910	+	5.57466i	−0.0777074	+	0.187602i	0.880252	+	0.474507i	$0.157374\pi$
$884$		0			0
$885$	−0.790790	+	0.327556i	−0.0265821	+	0.0110107i
$886$		0			0
$887$	39.2208	+	39.2208i	1.31691	+	1.31691i	0.916211	+	0.400696i	$0.131232\pi$
$887$	39.2208	+	39.2208i	1.31691	+	1.31691i	0.400696	+	0.916211i	$0.368768\pi$
$888$		0			0
$889$	−5.99686	+	5.99686i	−0.201128	+	0.201128i
$890$		0			0
$891$	−12.3213	−	29.7463i	−0.412780	−	0.996540i
$892$		0			0
$893$	20.3603	+	8.43353i	0.681333	+	0.282217i
$894$		0			0
$895$	−1.97296			−0.0659489
$896$		0			0
$897$	−6.21954			−0.207665
$898$		0			0
$899$	63.0350	+	26.1100i	2.10234	+	0.870816i
$900$		0			0
$901$	2.27491	+	5.49212i	0.0757882	+	0.182969i
$902$		0			0
$903$	−1.22088	+	1.22088i	−0.0406284	+	0.0406284i
$904$		0			0
$905$	−3.73178	−	3.73178i	−0.124049	−	0.124049i
$906$		0			0
$907$	−1.04757	+	0.433917i	−0.0347839	+	0.0144080i	−0.400008	−	0.916512i	$-0.630993\pi$
$907$	−1.04757	+	0.433917i	−0.0347839	+	0.0144080i	0.365224	+	0.930920i	$0.380993\pi$
$908$		0			0
$909$	−1.98413	+	4.79011i	−0.0658095	+	0.158878i
$910$		0			0
$911$		−	13.9472i		−	0.462092i	−0.972943	−	0.231046i	$-0.925785\pi$
$911$		−	13.9472i		−	0.462092i	0.972943	−	0.231046i	$-0.0742148\pi$
$912$		0			0
$913$			31.5706i			1.04483i
$914$		0			0
$915$	−0.323731	+	0.781555i	−0.0107022	+	0.0258374i
$916$		0			0
$917$	−18.1306	+	7.50993i	−0.598724	+	0.248000i
$918$		0			0
$919$	4.52081	+	4.52081i	0.149128	+	0.149128i	0.777728	−	0.628601i	$-0.216372\pi$
$919$	4.52081	+	4.52081i	0.149128	+	0.149128i	−0.628601	+	0.777728i	$0.716372\pi$
$920$		0			0
$921$	−1.65045	+	1.65045i	−0.0543843	+	0.0543843i
$922$		0			0
$923$	1.11718	+	2.69712i	0.0367726	+	0.0887768i
$924$		0			0
$925$	−3.45148	−	1.42965i	−0.113484	−	0.0470067i
$926$		0			0
$927$	−0.915231			−0.0300601
$928$		0			0
$929$	−30.1593			−0.989495			−0.494747	−	0.869037i	$-0.664739\pi$
$929$	−30.1593			−0.989495			−0.494747	+	0.869037i	$0.664739\pi$
$930$		0			0
$931$	−6.74030	−	2.79192i	−0.220904	−	0.0915016i
$932$		0			0
$933$	−2.31056	−	5.57818i	−0.0756443	−	0.182621i
$934$		0			0
$935$	−2.16543	+	2.16543i	−0.0708172	+	0.0708172i
$936$		0			0
$937$	−4.51510	−	4.51510i	−0.147502	−	0.147502i	0.629499	−	0.777001i	$-0.283260\pi$
$937$	−4.51510	−	4.51510i	−0.147502	−	0.147502i	−0.777001	+	0.629499i	$0.783260\pi$
$938$		0			0
$939$	3.31804	−	1.37438i	0.108280	−	0.0448511i
$940$		0			0
$941$	3.88909	−	9.38910i	0.126781	−	0.306076i	−0.847726	−	0.530435i	$-0.822029\pi$
$941$	3.88909	−	9.38910i	0.126781	−	0.306076i	0.974507	+	0.224359i	$0.0720287\pi$
$942$		0			0
$943$		−	76.9014i		−	2.50425i
$944$		0			0
$945$		−	0.541536i		−	0.0176162i
$946$		0			0
$947$	−7.57108	+	18.2782i	−0.246027	+	0.593962i	−0.997860	−	0.0653921i	$-0.979170\pi$
$947$	−7.57108	+	18.2782i	−0.246027	+	0.593962i	0.751833	+	0.659354i	$0.229170\pi$
$948$		0			0
$949$	−27.5073	+	11.3939i	−0.892923	+	0.369861i
$950$		0			0
$951$	−1.84727	−	1.84727i	−0.0599017	−	0.0599017i
$952$		0			0
$953$	−17.0976	+	17.0976i	−0.553846	+	0.553846i	−0.927548	−	0.373703i	$-0.878088\pi$
$953$	−17.0976	+	17.0976i	−0.553846	+	0.553846i	0.373703	+	0.927548i	$0.378088\pi$
$954$		0			0
$955$	2.07427	+	5.00772i	0.0671217	+	0.162046i
$956$		0			0
$957$	9.13714	+	3.78473i	0.295362	+	0.122343i
$958$		0			0
$959$	−14.4931			−0.468006
$960$		0			0
$961$	49.8178			1.60702
$962$		0			0
$963$	−11.5622	−	4.78920i	−0.372585	−	0.154330i
$964$		0			0
$965$	−1.59493	−	3.85050i	−0.0513426	−	0.123952i
$966$		0			0
$967$	−22.0097	+	22.0097i	−0.707784	+	0.707784i	−0.966069	−	0.258285i	$-0.916843\pi$
$967$	−22.0097	+	22.0097i	−0.707784	+	0.707784i	0.258285	+	0.966069i	$0.416843\pi$
$968$		0			0
$969$	4.57136	+	4.57136i	0.146853	+	0.146853i
$970$		0			0
$971$	−13.3118	+	5.51392i	−0.427196	+	0.176950i	−0.585913	−	0.810374i	$-0.699264\pi$
$971$	−13.3118	+	5.51392i	−0.427196	+	0.176950i	0.158718	+	0.987324i	$0.449264\pi$
$972$		0			0
$973$	5.30580	−	12.8093i	0.170096	−	0.410649i
$974$		0			0
$975$		−	4.67702i		−	0.149785i
$976$		0			0
$977$			41.9045i			1.34065i	0.742070	+	0.670323i	$0.233844\pi$
$977$			41.9045i			1.34065i	−0.742070	+	0.670323i	$0.766156\pi$
$978$		0			0
$979$	5.12874	−	12.3819i	0.163915	−	0.395726i
$980$		0			0
$981$	−34.6020	+	14.3326i	−1.10476	+	0.457606i
$982$		0			0
$983$	17.6158	+	17.6158i	0.561856	+	0.561856i	0.929834	−	0.367978i	$-0.119950\pi$
$983$	17.6158	+	17.6158i	0.561856	+	0.561856i	−0.367978	+	0.929834i	$0.619950\pi$
$984$		0			0
$985$	4.95485	−	4.95485i	0.157875	−	0.157875i
$986$		0			0
$987$	−0.376846	−	0.909787i	−0.0119951	−	0.0289588i
$988$		0			0
$989$	−32.0176	−	13.2621i	−1.01810	−	0.421711i
$990$		0			0
$991$	21.7432			0.690695			0.345348	−	0.938475i	$-0.387761\pi$
$991$	21.7432			0.690695			0.345348	+	0.938475i	$0.387761\pi$
$992$		0			0
$993$	−0.471209			−0.0149534
$994$		0			0
$995$	0.874391	+	0.362185i	0.0277201	+	0.0114820i
$996$		0			0
$997$	−6.80852	−	16.4372i	−0.215628	−	0.520572i	0.778642	−	0.627468i	$-0.215909\pi$
$997$	−6.80852	−	16.4372i	−0.215628	−	0.520572i	−0.994270	+	0.106896i	$0.965909\pi$
$998$		0			0
$999$	−1.03150	+	1.03150i	−0.0326352	+	0.0326352i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	896.2.u.c.337.7		52
4.3	odd	2		224.2.u.c.29.10	✓	52
32.11	odd	8		224.2.u.c.85.10	yes	52
32.21	even	8	inner	896.2.u.c.561.7		52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
224.2.u.c.29.10	✓	52	4.3	odd	2
224.2.u.c.85.10	yes	52	32.11	odd	8
896.2.u.c.337.7		52	1.1	even	1	trivial
896.2.u.c.561.7		52	32.21	even	8	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 896 = 2^{7} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	896.u (of order \(8\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.301186 + 0.124755i) q^{3} +(-0.107860 - 0.260396i) q^{5} +(-0.707107 + 0.707107i) q^{7} +(-2.04617 - 2.04617i) q^{9} +O(q^{10})\)	\(q+(0.301186 + 0.124755i) q^{3} +(-0.107860 - 0.260396i) q^{5} +(-0.707107 + 0.707107i) q^{7} +(-2.04617 - 2.04617i) q^{9} +(-3.69299 + 1.52969i) q^{11} +(1.11577 - 2.69371i) q^{13} -0.0918835i q^{15} +2.71818i q^{17} +(2.79192 - 6.74030i) q^{19} +(-0.301186 + 0.124755i) q^{21} +(-4.62688 - 4.62688i) q^{23} +(3.47936 - 3.47936i) q^{25} +(-0.735272 - 1.77510i) q^{27} +(-7.01178 - 2.90438i) q^{29} -8.98987 q^{31} -1.30311 q^{33} +(0.260396 + 0.107860i) q^{35} +(-0.290547 - 0.701441i) q^{37} +(0.672109 - 0.672109i) q^{39} +(8.31028 + 8.31028i) q^{41} +(4.89311 - 2.02679i) q^{43} +(-0.312116 + 0.753514i) q^{45} +3.02069i q^{47} -1.00000i q^{49} +(-0.339107 + 0.818676i) q^{51} +(2.02051 - 0.836925i) q^{53} +(0.796649 + 0.796649i) q^{55} +(1.68177 - 1.68177i) q^{57} +(-3.56490 - 8.60644i) q^{59} +(-8.50594 - 3.52327i) q^{61} +2.89372 q^{63} -0.821779 q^{65} +(-0.268430 - 0.111187i) q^{67} +(-0.816323 - 1.97078i) q^{69} +(-0.708001 + 0.708001i) q^{71} +(-7.22072 - 7.22072i) q^{73} +(1.48200 - 0.613865i) q^{75} +(1.52969 - 3.69299i) q^{77} +11.6234i q^{79} +8.05481i q^{81} +(3.02245 - 7.29684i) q^{83} +(0.707802 - 0.293181i) q^{85} +(-1.74951 - 1.74951i) q^{87} +(-2.37079 + 2.37079i) q^{89} +(1.11577 + 2.69371i) q^{91} +(-2.70762 - 1.12153i) q^{93} -2.05628 q^{95} -8.85759 q^{97} +(10.6865 + 4.42649i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 52 q+O(q^{10}) \) 52 * q	\( 52 q + 20 q^{23} + 24 q^{27} - 48 q^{33} + 24 q^{39} + 44 q^{43} + 40 q^{45} - 16 q^{51} - 36 q^{53} - 32 q^{55} - 32 q^{61} - 68 q^{63} + 80 q^{65} - 28 q^{67} - 32 q^{69} - 32 q^{75} - 12 q^{77} + 64 q^{85} + 56 q^{87} + 64 q^{95} - 72 q^{97} + 64 q^{99}+O(q^{100}) \) 52 * q + 20 * q^23 + 24 * q^27 - 48 * q^33 + 24 * q^39 + 44 * q^43 + 40 * q^45 - 16 * q^51 - 36 * q^53 - 32 * q^55 - 32 * q^61 - 68 * q^63 + 80 * q^65 - 28 * q^67 - 32 * q^69 - 32 * q^75 - 12 * q^77 + 64 * q^85 + 56 * q^87 + 64 * q^95 - 72 * q^97 + 64 * q^99

Introduction

L-functions

Modular forms

Varieties

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